Video coding method and apparatus for calculating motion vectors of the vertices of a patch of an image and transmitting information of horizontal and vertical components of the motion vectors

ABSTRACT

A method and apparatus for coding an image includes calculation of motion vectors of vertices of a patch in an image being encoded and transmitting information of horizontal and vertical components of the motion vectors of the vertices and information specifying that values of the horizontal and vertical components of a motion vector for each pixel in the patch are integral multiples of 1/d of a distance between adjacent pixels, where d is an integer not less than 2.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of application Ser. No.11/155,570, filed Jun. 20, 2005, now U.S. Pat. No. 7,133,454; which is acontinuation of application Ser. No. 10/342,273, filed Jan. 15, 2003,now U.S. Pat. No. 6,928,117; which is a continuation of application Ser.No. 09/994,728, filed Nov. 28, 2001, now U.S. Pat. No. 6,542,548; whichis a divisional application of application Ser. No. 09/863,428, filedMay 24, 2001, now U.S. Pat. No. 6,516,033; which is a divisional ofapplication Ser. No. 09/626,788, filed Jul. 26, 2000, now U.S. Pat. No.6,285,713; which is a continuation of application Ser. No. 09/364,255,filed Jul. 30, 1999, now U.S. Pat. No. 6,134,271; which is acontinuation of application Ser. No. 08/903,199, filed Jul. 15, 1997,now U.S. Pat. No. 5,963,259; which is a continuation of application Ser.No. 08/516,218, filed Aug. 17, 1995, now U.S. Pat. No. 5,684,538, thecontents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a video-coding/decoding system and avideo coder and a video decoder used with the same system forimplementing a motion compensation method in which all the pixelsassociated with the same patch are not restricted to have a commonmotion vector and in which the horizontal and vertical components of amotion vector of a pixel can assume an arbitrary value other than anintegral multiple of the distance between adjacent pixels.

2. Description of the Related Art

In the high-efficiency coding and decoding of image sequences, a motioncompensation method utilizing the analogy between temporally-proximateframes is well known to have a great advantage in compressing the amountof information.

FIGS. 1A and 1B are diagrams showing a general circuit configuration ofa video coder 1 and a video decoder 2 to which the motion compensationmethod described above is applied.

In FIG. 1A, a frame memory 2-1 has stored therein a reference image Rproviding a decoded image of the previous frame already coded. A motionestimation section 3-1 estimates a motion and outputs motion informationusing the original image I of the current frame to be coded and thereference image R read out of the frame memory 2-1. A predicted imagesynthesis circuit 4-1 synthesizes a predicted image P for the originalimage I using the motion information and the reference image R. Asubtractor 5-1 calculates the difference between the original image Iand the predicted image P and outputs a prediction error. The predictionerror is subjected to the DCT conversion or the like at a predictionerror coder 6-1, and transmits the prediction error information togetherwith the motion information to the receiving end. At the same time, theprediction error information is decoded by the inverted DCT conversionor the like at a prediction error decoder 7-1. An adder 8-1 adds thecoded prediction error to the predicted image P and outputs a decodedimage of the current frame. The decoded image of the current frame isnewly stored in the memory 2-1 as a reference image R.

In FIG. 1B, a frame memory 2-2 has stored therein a reference image Rproviding a decoded image of the previous frame. A synthesis circuit 4-2synthesizes a predicted image P using the reference image R read out ofthe frame memory 2-2 and the motion information received. The receivedprediction error information is decoded by being subjected to theinverse DCT conversion or the like by a prediction error decoder 7-2. Anadder 8-2 adds the decoded prediction error to the predicted image P andoutputs a decoded image of the current frame. The decoded image of thecurrent frame is newly stored in the frame memory 2-2 as a referenceimage P.

A motion compensation method constituting the main stream of the currentvideo coding and decoding techniques depends on the “block matching ofhalf-pixel accuracy” employed by MPEG1 and MPEG2 providing theinternational standard of video coding/decoding method.

In the “block matching of half-pixel accuracy”, the original image ofthe current frame to be coded is segmented into a number n of blocks atthe motion estimation section 3-1 in FIG. 1A, and a motion vector isdetermined for each block as a motion information. The horizontal andvertical components of this motion vector have a minimum unit lengthequal to one-half of the distance between horizontally and verticallyadjacent pixels, respectively. In the description that follows, let thehorizontal component of the motion vector of the ith block(1.ltoreq.i.ltoreq.n) be ui and the vertical component thereof be vi. Ina method most widely used for estimating the motion vector (ui,vi), asearch range such as −15.ltoreq.ui.ltoreq.15, −15.ltoreq.vi.ltoreq.15 ispredetermined, and a motion vector (ui,vi) which minimizes theprediction error Ei(ui,vi) in the block is searched for. The predictionerror Ei(ui,vi) is expressed by Equation 1 using a mean absolute error(MAE) as an evaluation standard. Ei.function.(ui,vi)=1Ni.times.(x,y).di-electcons.B1.times..times.I.function.(x,y)−R.function.(x−ui,y−vi) (1)

In Equation 1, l(x,y) denotes the original image of the current frame tobe coded, and R(x,y) a reference image stored in memory. In thisequation, it is assumed that pixels exist at points of which the x and ycoordinates are an integer on the original image l and the referenceimage R. Bi designates the pixels contained in the ith block of theoriginal image I, and Ni the number of pixels contained in the ith blockof the original image I. The process of evaluating the prediction errorfor motion vectors varying from one block to another and searching for amotion vector associated with the smallest prediction error is calledthe matching. Also, the process of calculating Ei(ui,vi) for all vectors(ui,vi) conceivable within a predetermined search range and searchingfor the minimum value of the vector is called the full search.

In the motion estimation for the “block matching of half-pixelaccuracy”, ui and vi are determined with one half of the distancebetween adjacent pixels, i.e., ½ as a minimum unit. As a result,(x−ui,y−vi) is not necessarily an integer, and a luminance value of apoint lacking a pixel must actually be determined on the reference imageR when calculating the prediction error using Equation 1. The processfor determining the luminance value of a point lacking a pixel is calledthe interpolation, and the point where interpolation is effected isreferred to as an interpolated point or an intermediate point. Abilinear interpolation is often used as an interpolation process usingfour pixels around the interpolated point.

When the process of bilinear interpolation is described in a formula,the luminance value R(x+p,y+q) at the interpolated point (x+p,y+q) ofthe reference image R can be expressed by Equation 2 with the fractionalcomponents of the coordinate value of the interpolated point given as pand q(0.ltoreq.p.ltoreq.1,0.ltoreq.q<1).R(x+p,y+q)=(1−q){(1−p)R(x,y)+pR(x+1,y)}+q{(1−p)R(x,y+1)+pR(x+1,y+1)}(2).

In the motion estimation by “block matching of half-pixel accuracy”, atwo-step search is widely used in which, first, the full-search ofsingle-pixel accuracy is effected for a wide search range to estimate amotion vector approximately, followed by the full search of half-pixelaccuracy for a very small range defined by, say, plus/minus a half pixelin horizontal and vertical directions around the motion vector. In thesecond-step search, a method is frequently used in which the luminancevalue of an interpolated point on the reference image R is determined inadvance. An example of the process according to this method is shown inFIGS. 2A, B, C and D. In this example, a block containing four pixelseach in longitudinal and lateral directions is used. In FIGS. 2A, B, Cand D, the points assuming an integral coordinate value and originallyhaving a pixel in a reference image are expressed by a white circle,large circle, and the interpolated points for which a luminance value isnewly determined are represented by X. Also, the pixels in a block ofthe original image of the current frame are expressed by a white squarequadrature. The motion vector obtained by the first-step search isassumed to be (uc,vc). FIG. 2A shows the state of matching when themotion vector is (uc,uv) in the first-step search. The prediction erroris evaluated between each pair of large circle and quadrature.overlapped. FIGS. 2B, C and D show the case in which the motion vectoris (uc+½,vc), (uc+½,vc+½), (uc−½,vc−½) in the second-step search. Theprediction error is evaluated between each overlapped pair of X andquadrature. in FIGS. 2B, C and D. As seen from these drawings, in thecase where the range for the second-step search is ±½ pixel each inlongitudinal and lateral directions, the matching process for eightmotion vectors ((uc,vc+½), (uc+½,vc), (uc+½,vc+½), (uc−½, vc.±.½) can beaccomplished by determining the luminance value of 65(=the number of Xin each drawing) interpolated points in advance. In the process, all theinterpolated points of which the luminance value was determined are usedfor matching.

On the other hand, assuming that the interpolation calculation is madeon a reference image each time of matching, a total of 128 (=16.times.8,in which 16 is the number of white squares in FIGS. 2B, C and D, and 8is the number of times the matching is made) interpolations would berequired.

As described above, the number of interpolation operations can bereduced by determining the luminance value of the interpolated points onthe reference image R in advance by reason of the fact that the sameinterpolated point on the reference image R is used a plurality oftimes.

Also, in the “block matching of half-pixel accuracy”, a predicted imageis synthesized using the relation of Equation 3 in the synthesiscircuits 4-1, 4-2 shown in FIGS. 1A and 1B.P(x,y)=R(x−ui,y−vi),(x,y).epsilon.Bi(1.ltoreq.i.ltoreq.n) (3)

In Equation 3, P(x,y) shows an original image I(x,y) of the currentframe to be coded which is predicted by use of the reference imageR(x,y) and the motion vector (ui,vi). Also, assuming that the predictedimage P is segmented into a number n of blocks corresponding to theoriginal image I, Bi represents a pixel contained in the ith block ofthe predicted image P.

In the “block matching of half-pixel accuracy”, as described above, thevalue of (x−ui,y−vi) is not necessarily an integer, and therefore theinterpolation process such as the bilinear interpolation using Equation2 is carried out in synthesizing a predicted image.

The “block matching of half-pixel accuracy” is currently widely used asa motion compensation method. Applications requiring an informationcompression ratio higher than MPEG1 and MPEG2, however, demand an evenmore sophisticated motion compensation method. The disadvantage of the“block matching” method is that all the pixels in the same block arerequired to have the same motion vector.

In order to solve this problem, a motion compensation method allowingadjacent pixels to have different motion vectors has recently beenproposed. The “motion compensation based on spatial transformation”which is an example of such a method is briefly explained below.

In the “motion compensation based on spatial transformation”, therelation between the predicted image P and the reference image R insynthesizing a predicted image at the synthesis circuit 4-1, 4-2 inFIGS. 1A and 1B is expressed by Equation 4 below.P(x,y)=R(fi(x,y),gi(x,y)),(x,y).epsilon.Pi(1.ltoreq.i.ltoreq.n)  (4).

In Equation 4, on the assumption that the predicted image P is segmentedinto a number n of patches corresponding to the original image I, Pirepresents a pixel contained in the ith patch of the predicted image P.Also, the transformation functions fi(x,y) and gi(x,y) represent aspatial correspondence between the predicted image P and the referenceimage R. The motion vector for a pixel (x,y) in Pi can be represented by(x−fi(x,y),y−gi(x,y)). The predicted image P is synthesized bycalculating the transformation functions fi(x,y), gi(x,y) with respectto each pixel in each patch and determining the luminance value ofcorresponding points in the reference image R in accordance withEquation 4. In the process, (fi(x,y), gi(x,y)) is not necessarily aninteger, and therefore the interpolation process such as the bilinearinterpolation is performed using Equation 3 as in the case of the “blockmatching of half-pixel accuracy”.

The “block matching” can be interpreted as a special case of the “motioncompensation based on spatial transformation” in which thetransformation function is a constant.

Nevertheless, the words “motion compensation based on spatialtransformation” as used in the present specification are not assumed toinclude the “block matching”.

Examples of the transformation functions fi(x,y), gi(x,y) in the “motioncompensation based on spatial transformation” include the case using theaffine transformation shown in Equation 5 (refer to “Basic Study ofMotion Compensation Based on Triangular Patches” by Nakaya, et al.,Technical Report of IEICE, IE90-106, H2-03) shown belowfi(x,y)=ai1x+ai2y+ai3 gi(x,y)=ai4x+ai5y+ai6 (5) the case using thebilinear transformation given in Equation 6 (G. J. Sullivan and R. L.Baker, “Motion compensation for video compression using control gridinterpolation”, Proc. ICASSP '91, M9.1, pp. 2713-2716, 1991-05) shownbelow fi(x,y)=bi1xy+bi2x+bi3y+bi4 gi(x,y)=bi5xy+bi6x+bi7y+bi8 (6) andthe case using the perspective transformation given in Equation 7 (V.Seferdis and M. Ghanbari, “General approach to block-matching motionestimation”, Optical Engineering, vol. 32, no. 7, pp. 1464-1474,1993-07) shown below fi.function.(x,y)=ci.times..times.4.times..times.x+ci.times..times.5.times..times.y+ci.times..times.6ci.times..times.1.times..times.x+ci.times..times.2.times..times.y+ci.times..times.3.times..times.gi.function.(x,y)=ci.times..times.7.times..times.x+ci.times..times.8.times.y+ci.times..times.9ci.times..times.1.times..times.x+ci.times..times.2.times..times.y+ci.times..times.3 (7).

In Equations 5, 6 and 7, aij, bij, cij (j: 1 to 9) designate motionparameters estimated for each patch as motion information at the motionestimation section 3-1 in FIG. 1A. An image identical to the predictedimage P produced at the synthesis circuit 4-1 of the video coder 1 canbe obtained at the synthesis circuit 4-2 of the video decoder 2 at thereceiving end in such a manner that information capable of specifyingthe motion parameter of the transformation function for each patch insome form or other is transmitted by the video coder 1 as motioninformation to the video decoder 2 at the receiving end. Assume, forexample, that the affine transformation (Equation 5) is used as thetransformation function and the patch is triangular in shape. In such acase, six motion parameters can be transmitted directly as motioninformation. Alternatively, the motion vectors of three vertices of apatch may be transmitted so that six motion parameters indicated byEquation 5 are calculated from the motion vectors of the three verticesat the receiving end. Also, in the case where the bilineartransformation (Equation 6) is used as the transformation function, theemployment of a quadrilateral patch makes it possible to transmit thedesired one of eight motion parameters and the motion vectors of fourvertices of the patch.

The following explanation refers to the case using the affinetransformation (Equation 5) as the transformation function. Thisexplanation applies substantially directly with equal effect to the casewhere other transformations (Equation 6, 7, etc.) are employed.

Even after a transformation function is established, many variations areconceivable for the “motion compensation based on spatialtransformation”. An example is shown in FIG. 3. In this case, the motionvector is restricted to continuously change at the patch boundary.First, an original image 1202 of the current frame is segmented into aplurality of polygonal patches, thereby constituting a patch-segmentedoriginal image 1208. The vertices of these patches are called the gridpoints, each of which is shared by a plurality of patches. A patch 209in FIG. 3, for example, is composed of grid points 210, 211, 212, whichfunction also as vertices of other patches. After the original image1202 is segmented into a plurality of patches in this way, motionestimation is performed. In the shown example, motion estimation isperformed with a reference image R201 with respect to each grid point.As a result, each patch is deformed on the reference image R203 aftermotion estimation. The patch 209, for instance, corresponds to thedeformed patch 204. This is by reason of the fact that the grid points205, 206, 207 on the original image 1208 are estimated to have beentranslated to the grid points 210, 211, 212 respectively on thereference image R203 as a result of motion estimation. Since most of thegrid points are shared by multiple patches in this example, the amountof transmitted data can be reduced by transmitting the motion vectors ofthe grid points rather than transmitting the affine transformationparameters of each patch.

In the “motion compensation based on spatial transformation”, as in the“block matching”, it is pointed out that the motion estimation based onmatching is effective. An example algorithm for motion estimation basedon matching is described below. This scheme is called the “hexagonalmatching” and is effectively applied to the case where the motion vectorcontinuously changes at the patch boundary. This scheme is configured oftwo processes:

(1) Coarse motion estimation of grid points by “block matching”; and

(2) Correction of motion vector by “refinement algorithm”.

In process (1), the block matching is applied to a block of a given sizecontaining a grid point, and the motion vector of this block isdetermined as a coarse motion vector for the grid points existing in theparticular block. The object of process (1) is nothing but to determinea coarse motion vector of a grid point and is not always achieved usingthe block matching. The manner in which process (2) is carried out isshown in FIG. 4. FIG. 4 shows a part of a patch and grid points in thereference image R which corresponds to the reference image R203 in FIG.3. Thus, changing the position of a grid point in FIG. 4 is indicativeof changing the motion vector of the same grid point. In refining themotion vector of the grid point 301, the first thing to do is to fix themotion vectors of the grid points 303 to 308 representing the verticesof a polygon 302 configured of all the patches involving the grid point301. The motion vector of the grid point 301 is changed with apredetermined search range in this way. For example, the grid point 301is translated to the position of the grid point 309. As a result, theprediction error within each patch contained by the polygon 302 alsoundergoes a change. The motion vector minimizing the prediction errorwithin the polygon 302 in the search range is registered as a refinedmotion vector of the grid point 301. The refinement of the motion vectorof the grid point 301 is thus completed, and a similar operation ofrefinement is continued by translating to another grid point. Once allthe grid points are refined, the prediction error can be further reducedby repeating the refinement from the first grid point. The appropriatenumber of repetitions of the refinement process is reported to be two orthree.

A typical search range for the refinement algorithm is .+−.3 pixels ineach of horizontal and vertical directions. In such a case, a total of49 (=7.times.7) matching operations are performed for each grid point inthe polygon 302. Since each patch is involved in the refinementalgorithm for three grid points, on the other hand, it follows that atotal of 147 (=49.times.3) evaluations of prediction error is performedfor each pixel in a patch. Further, each repetition of this refinementprocess increases the number of prediction error evaluationscorrespondingly. Consequently, each time of prediction error evaluation,interpolation computations are carried out for the interpolated pointsinvolved on the reference image, thereby enormously increasing theamount of computations.

The problem of interpolation computation in the motion estimation forthe “motion compensation based on spatial transformation” is complicateddue to the essential difference thereof from the similar problem in themotion estimation for the “block matching at half-pixel accuracy”. Inthe “motion compensation based on spatial transformation”, even when thehorizontal and vertical components of the motion vector of each gridpoint are restricted to an integral multiple of ½, the horizontal andvertical components of the motion vector of each pixel in each patch arenot necessarily an integral multiple of ½. Also, in view of the factthat the components below the decimal point of the motion vector foreach pixel in each patch generally can assume an arbitrary value, theluminance value of the same interpolated point on the reference image Ris rarely used a plurality of times in the matching operation.

The feature of the “motion compensation based on spatial transformation”is that a numerical operation is required for determining a motionvector for each pixel. In the case where the computation accuracy variesbetween the transmitting and receiving ends in computing a motion vector(transformation function), a mismatch may occur in which the predictedimage P obtained at the synthesis circuit 4-1 of the video coder 1 isdifferent from the predicted image P produced from the synthesis circuit4-2 of the video decoder 2. This mismatch of the predicted image P hasthe property of accumulating at the receiving end. Even when there isonly a small error for each frame, therefore, the quality of the decodedimage output from the video decoding circuit 2 may be seriously affectedin the end. This problem is not posed by the “block matching” in whichall the pixels in a block follow the same motion vector and thisparticular motion vector is coded and transmitted directly as motioninformation.

An example of employing the affine transformation (Equation 5) as atransformation function to cope with this problem is explained. A methodof solving such a problem is by enhancing the computation accuracy ofEquation 5 sufficiently to reduce the computation error of Equation 5sufficiently below the quantization step size of the luminance value. Acase using this solution is studied below.

Assume, for example, that the luminance value is quantized in 8 bitswith the quantization step size of 1 and that the maximum value of theluminance value is 255 (11111111) and the minimum value thereof is 0(00000000). Also, assume that the luminance values of four adjacentpixels on the reference image P are R(0,0) 0, R(0,1)=0, R(1,0)=255, andR(1,1)=255, respectively. Further, it is assumed that the computation ofEquation 5 is carried out to determine fi(x,y) when the horizontal andvertical coordinates of a point on the reference image R correspondingto a pixel P(x,y) on the predicted image P are given by 0<gi(x,y)<1 and0<fi(x,y)<1, respectively. This condition is hereinafter referred to asthe worst condition.

Under this worst condition, a computation error more than 1/255 inmagnitude of fi(x,y) always leads to an error of the quantized value ofthe luminance. For a mismatch to be prevented, therefore, both the videocoder 1 and the video decoder 2 must be fabricated in such a manner asto secure the computation error of Equation 5 sufficiently smaller than1/255. Improving the computation accuracy, however, generally leads toan increased number of digits for internal expression of a numericalvalue, thereby further complicating the computation process. In themotion compensation process, Equation 5 is computed so frequently thatan increased complication of this computation process has a seriousadverse effect on the total amount of information processed.

SUMMARY OF THE INVENTION

With the “motion compensation based on spatial transformation”, motionestimation based on matching poses the problem of a greatly increasedamount of computations required for interpolation of luminance values atpoints lacking a pixel on the reference image R. A more complicatedcomputation operation is another problem which will be posed if thecomputation accuracy for synthesizing each predicted image P in thevideo coder and the video decoder is to be improved to accommodate amismatch between a predicted image P obtained at the sending end and apredicted image P obtained at the receiving end.

An object of the present invention is to realize a motion estimationprocess with a small amount of computations by reducing the number ofcalculations for interpolation of luminance values.

Another object of the invention is to provide a method of reducing thecomputation accuracy required for computing the transformation functionat the time of synthesizing a predicted image P and also preventing themismatch between the predicted images P attributable to the computationaccuracy of the transformation function.

Prior to motion estimation, a high-resolution reference image R′ isprepared for which the luminance value of a point having x and ycoordinates equal to an integral multiple of 1/m1 and 1/m2 (m1 and m2are positive integers) respectively is determined by interpolation onthe reference image R. It follows therefore that in the high-resolutionreference image R′, pixels exist at points whose x and y coordinatevalues are an integral multiple of 1/m1 and 1/m2 respectively. In thecase where the luminance value of the reference image R at a positionhaving a coordinate value other than an integer becomes required in theprocess of motion estimation, such a value is approximated by theluminance value of a pixel existing at a position nearest to theparticular coordinate in the high-resolution reference image R′. Theobject of reducing the number of interpolation computations thus isachieved.

In the above-mentioned process for preparing the high-resolutionreference image R′, interpolation computations in the number ofm1.times.m2−1 per pixel of the original image I are required. Once theinterpolation process for achieving a high resolution is completed,however, the motion estimation process does not require any furthercomputations for interpolation. In the case of the “motion compensationbased on spatial transformation” described with reference to the relatedart above, more than 147 interpolation computations is required for eachpixel in the motion estimation. When it is assumed that m1=m2=2, thenumber of required interpolation computations is not more than three perpixel or about one fiftieth of the conventional requirement. Even whenm1=m2=4, the number of required interpolation computations is only 15,which is as small as about one tenth. The computation amount thus can bereduced remarkably.

Also, assume that the horizontal and vertical components of the motionvector of each pixel used for synthesizing the predicted image P in thevideo coder and the video decoder are defined to take a value equivalentonly to an integral multiple of 1/d1 or 1/d2 (d1 and d2 being integers)respectively of the distance between adjacent pixels. The object ofreducing the required computation accuracy of the transformationfunction and preventing a mismatch is thus achieved.

In the case where the above-mentioned rule on motion vectors isemployed, the magnitude of the computation error of the transformationfunction fi(x,y) always leading to an error of the quantization value ofluminance under the “worst condition” described with reference to therelated art above is 1/d1. Suppose d1=4, for example, the risk ofcausing a mismatch of the predicted images under the “worst condition”is maintained substantially at the same level even when the computationaccuracy of fi(x,y) is reduced by 6 bits as compared with the proposedsolution described above with reference to the related art.

The foregoing and other objects, advantages, manner of operation andnovel features of the present invention will be understood from thefollowing detailed description when read in conjunction with theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a diagram showing an example of a conventional video coder.

FIG. 1B is a diagram showing an example of a conventional video decoder.

FIG. 2A to 2D are diagrams showing an example process of the second-stepsearch in the “block matching of half-pixel accuracy”.

FIG. 3 is a diagram showing an example process for motion estimation inthe “motion compensation based on spatial transformation”.

FIG. 4 is a diagram showing the process according to a scheme called the“hexagonal matching” as an example of motion estimation operation in the“motion compensation based on spatial transformation”.

FIG. 5 is a diagram showing an example of a video coder utilizing ahigh-resolution reference image.

FIG. 6 is a diagram showing an example of an interpolation circuit usingthe bilinear interpolation for interpolation of luminance values.

FIG. 7 is a diagram showing an example circuit for producing a luminancevalue in a high-resolution reference image from the result ofcomputations of the transformation function in a matching circuit.

FIG. 8 is a diagram showing the range of pixels used for refinement inthe “hexagonal matching”.

FIG. 9 is a diagram showing the range of pixels additionally requiredfor performing the refinement following the adjacent grid points in therefinement process for the “hexagonal matching”.

FIG. 10 is a diagram showing a video coder including a motion estimationsection for performing motion estimation by improving the resolution ofa reference image while fetching the required portions of the originalimage of the current frame and a reference image little by little.

FIG. 11 is a diagram showing the case in which parallel processing isintroduced to a scheme used for performing motion estimation whilefetching the required portion of the original image of the current frameand a reference image little by little.

FIG. 12 is a diagram showing an example translation and deformation of apatch in the motion compensation based on spatial transformation.

FIG. 13 is a diagram showing an example method of computing thetransformation function when the horizontal and vertical components of amotion vector are restricted to an integer multiple of 1/4(d=4).

FIG. 14 is a diagram showing an example scheme for determining the valueof 1/d providing a minimum unit of the pixel motion vector bycommunication between the sending and receiving ends before transmissionof video data.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

A method of performing the motion estimation operation by improving theresolution of the whole reference image R in a video coder 1 will beexplained as a first embodiment. First, the luminance value of a pointlacking a pixel on the reference image R is interpolated to form ahigh-resolution reference numeral R′. Assuming that the bilinearinterpolation (Equation 3) is used as an interpolation scheme for theluminance value, the high-resolution reference numeral R′ is given byEquation 8. R′(x+sm.times..times.1,y+tm.times..times.2=(1−tm.times..times.2).times.{(1−sm.times..times.1).times.R.function.(x,y)+sm.times..times.1 .times.R.function.(x+1,y)}+tm.times..times.2 .times.{(1−sm.times..times.1.times.R.function.(x,y+)+sm.times..times.1 .times.R.function.(x+1,y+1)}(8) where it is assumed that s and t are an integral number and that0.ltoreq.s.ltoreq.m1 and 0.ltoreq.t.ltoreq.m2. On the high-resolutionreference image R′, pixels are assumed to exist at points where all ofx, y, s and t are an integral number.

The points where s=t=0 corresponds originally to pixels existing on thereference image R, and the luminance value of other points can bedetermined by interpolation.

In the description that follows, an embodiment will be explained withreference to the case in which m1=m2=m (m: positive integral number) forthe sake of simplicity.

An example of an video coder 1 utilizing the high-resolution referenceimage R′ is shown in FIG. 5. The arrows in FIG. 5 indicate a data flowwhile address signals are not shown. In this system, a motion estimationsection 401 is in charge of motion estimation. A reference image 404,after being processed at a reference image interpolation circuit 405 forimproving the resolution, is stored in a frame memory 407 as ahigh-resolution reference image R′ 406 thereby to provide anapproximated luminance value 408 to a matching circuit 409. On the otherhand, the original image 1402 of the current frame is stored in theframe memory 403 and utilized for motion estimation at the matchingcircuit 409. The motion information 415, which is output from thematching circuit 409 is transmitted to the receiving end, is alsoutilized for synthesizing a predicted image P410 at a synthesis circuit4-1 in the video coder 1. The difference between the synthesizedpredicted image P410 and the original image I411 of the current frame isdetermined at a subtrator 5-1 and coded at a prediction error coder 6-1as a prediction error 413 while being transmitted as a prediction errorinformation 416. In the conventional method, the computation of thetransformation function, the interpolation and the evaluation of theprediction error are all performed at a matching circuit. According tothis embodiment, by contrast, the amount of computations is reduced byperforming the interpolation operation in advance at the interpolationcircuit 405. Also, by using the high-resolution reference image R′, thecomputation accuracy required for the computation of a transformationfunction at the matching circuit 409 can be reduced. Further, therelated process can be simplified. This is due to the fact that in thecase of an error occurred in the computation of a transformationfunction, the result of motion estimation is not affected as far as thepixels used as an approximated value on the high-resolution referenceimage R′ are not different. All the pixels on the high-resolutionreference image R′ of which the luminance value is determined byinterpolation are not necessarily used for the matching operation. Thispoint is different from the example of the “block matching of half-pixelaccuracy” described above.

An example of the interpolation circuit 405 using the bilinearinterpolation (Equation 8) for the interpolation of a luminance value isshown in FIG. 6 assuming that m=2. Also in this diagram, the arrowsindicate the data flow, and the reference numerals identical to those inFIG. 5 denote the same component elements respectively. The inputreference image signal 404 is assumed to apply a luminance value ofpixels from left to right for each line downward. This signal is appliedto a circuit including two pixel delay circuits 501, 502 and a linedelay circuit 501, thereby producing luminance values 504 to 507 of fourpixels adjacent in the four directions. These luminance values 504 to507 are multiplied by a weighting coefficient corresponding to theinterpolation position using multipliers 508 to 511 respectively, andthe result is applied to adders 512 to 514. The result of addition isfurther applied to an adder 515 and a shift register 516 to achieve thedivision by 4 (four) and rounding of the quotient. As a result of theaforementioned process, the luminance values 517 to 520 for the fourpixels of the high-resolution reference image R′ can be obtained as anoutput 406.

FIG. 7 shows an example circuit for producing an approximated valueR′(x′,y′) of the luminance value at an interpolated point of thereference image using the high-resolution reference image R′ in thematching circuit 409. The reference numerals identical to those in FIG.5 denote the same component elements respectively. In the case underconsideration, the fixed point binary representation of the coordinatesfi(x,y) 601 and gi(x,y) 602 on the reference image R are assumed to begiven by calculating the transformation function (Equations 5 to 7).Also, it is assumed that m is 2 as in the case of FIG. 6 and that thehigh-resolution reference image R′ is stored in the frame memory 407.The coordinate values fi(x,y) 601 and gi(x,y) 602 are applied through anadder 603 for adding ¼ and a circuit 604 that omits the figures at thesecond and lower order binary places and thus are converted into aninteger multiple of ½. The resulting coordinate values x′605 and y′606correspond to the coordinate values at a point having a pixel on thehigh-resolution reference image R′. These coordinate values x′605 andy′606 are converted into an address of the frame memory 407 by acoordinate-address conversion circuit 607, thereby producing an intendedapproximated luminance value 408 from the frame memory 407. In the caseunder consideration, the components of the third and lower places belowdecimal point of the computation result of the transformation functionare not used at all. It follows therefore that any computation error ina range not affecting the second and higher places below decimal pointof the computation result of the transformation function does not affectthe result of motion estimation. This is due to the fact that, asdescribed above, the use of the high-resolution reference image R′ hasreduced the computation accuracy required of the transformation functioncomputation.

In the first embodiment, although the number of interpolationcomputations is reduced, a memory capable of storing an image four timeslarger than the reference image R is required as the frame memory 407for storing the high-resolution reference image R′. In view of this, asecond embodiment is described below, in which although the number ofinterpolation computations required is increased as compared with thefirst embodiment, the required memory capacity is reduced.

In the second method, while the required portion of the original image Iand the reference image R of the current frame are fetched little bylittle, the reference image R is interpolated and used for motionestimation. The distance between adjacent pixels is assumed to be unityfor both horizontal and vertical directions on the original image I ofthe current frame and the reference image R. The description below isbased on the assumption that the “hexagonal matching” is used for motionestimation, and is centered on a circuit for executing the refinementoperation in the “hexagonal matching”. The coarse motion estimation ofgrid points which constitutes another process for the “hexagonalmatching”, as already explained, is carried out by executing the “blockmatching” for a block containing the grid points.

FIG. 8 shows the position of grid points 703 to 711 in a portion of theoriginal image I of the current frame. Assume that the interval betweengrid points is Ng in horizontal and vertical directions and the searchrange of the motion vector for each grid point is +−.Ns in horizontaland vertical directions. The “hexagonal matching” for the grid point 703can be refined by using the pixels contained in the range 701 of 2Ng+2Nsin horizontal and vertical-directions of the reference image R and therange 702 (shadowed portion) of 2Ng in horizontal and verticaldirections of the original image of the current frame. Actually,however, a smaller range will do, even though a square area is used tosimplify the process. A device for performing the refinement process canthus perform subsequent processes independently of the external framememory by reading the luminance values of the pixels contained in thisrange in advance. Also, in this case, if the grid point 708 is refinedbefore the grid point 703, it follows that a part of the pixels of therange 701 and range 702 has already been read in the refinement device.In such a case, as shown in FIG. 9, only the range 801 of the referenceimage R and the range 802 of the original image I of the current frameare additionally read. In FIG. 9, the reference numerals identical tothose in FIG. 8 designate the same component parts respectively. In theprocess of additional reading, a portion of the data on the pixels onthe original image I and the reference image R used for motionestimation of the grid point 708 becomes unnecessary. The data of theranges 801 and 802, therefore, can be written on a memory which thus farcontained the same data portion.

In this way, the process can be simplified by reading only the datawhich becomes newly required each time of movement from left to right ofa grid point for motion estimation.

FIG. 10 is a diagram showing an example of the video coder 1 including amotion estimation section 909 for refining the “hexagonal matching”according to the method shown in FIGS. 8 and 9. In FIG. 10, the arrowsindicate the flow of data, and the same reference numerals as those ofFIG. 5 designate the same component elements respectively. The motionestimation section 909 is configured differently from but has the samefunction as the motion estimation section 401 in FIG. 5. The originalimage I402 of the current frame and the reference image R404 of theinput are stored in frame memories 1-1 and 2-1 respectively. First, ancoarse motion estimation of a grid point is executed at a circuit 902,and according to the motion vector thus determined, the coordinateinformation of the grid point on the reference image is stored in a gridpoint coordinate memory 904. Then, a refinement process section 905refines the “hexagonal matching”. The description below deals with therefinement process to be performed for the grid point 703 as in theexample of FIG. 9 immediately after the grid point 708 was refined. Therefinement process section 905 includes an interpolation circuit 907 anda matching circuit 906. First, the interpolation circuit 907 reads outthe luminance value of pixels in a range (the range 801 in the case ofFIG. 9) newly required from the frame memory 2-1 in which a referenceimage is stored. This information is interpolated and a high-resolutionreference image R′ in a range required for motion estimation is thusproduced. This high-resolution reference image R′ is applied to thematching circuit 906. The matching circuit 906 similarly reads theluminance value in a range (the range 802 in the case of FIG. 9) newlyrequired from the frame memory 1-1 of the original image I of thecurrent frame. The matching circuit 906 has a private memory for storingthe original image I of the current frame and the high-resolutionreference image R′ in a range required for refinement, and carries outthe matching process using the same memory. The matching circuit 906further reads the newly required coordinate information (coordinateinformation for the grid points 704, 706, 711 for the example of FIG. 9,because the coordinate information for the grid points 707, 708 and 710are used in the previous process) for grid points in the reference imageR from the coordinate point coordinate memory 904, thereby performingthe refinement of the “hexagonal matching”. In accordance with theresult of this process, the refined coordinate of a grid point on thereference image R (the coordinate of the grid point 703 in the exampleof FIG. 9) is written in the grid point coordinate memory 904. Thisparticular process completes the refinement of the grid point 703, andthe refinement process section 905 proceeds to the refinement of thegrid point 704. Upon completion of the entire refinement process, theinformation stored in the grid point coordinate memory 904 is convertedinto a motion vector for each grid point at a vector computation circuit908 and output as motion information 415.

FIG. 11 shows an example of introducing the parallel operation to theprocess at the motion estimation section 909 of the video decoder 1shown in FIG. 10. The reference numerals in FIG. 11 identical to thosein FIG. 10 designate the same component parts respectively as in FIG.10. In this example, there are a plurality of refinement processsections for refining the “hexagonal matching”, and each section sharesthe processing operation. A common data bus 1001 and an address bus 1002are used for reading the luminance value information from the framememory 2-1 and the frame memory 1-1 which store the original image I ofthe current frame and the reference image R. On the other hand, a commondata bus 1005 and an address bus 1004 are used for reading informationfrom or writing information into the grid point coordinate memory 904which stores the coordinates of the grid points on the reference image.Through these buses, information is transferred by a circuit 902 forperforming coarse motion estimation of grid points and circuits 905 and1003 for performing the refinement operation for the “hexagonalmatching”. The refinement process sections 905 and 1003 have the sameconfiguration. The refinement operation can be carried out at higherspeed by adding a refinement process section of a similar configuration.The refinement process sections can operate substantially independentlyof each other except for the processes of reading the luminance valueinformation and reading/writing the grid point coordinate information.Therefore, a parallel process is secured while avoiding conflicts inmemory access.

In the embodiments shown in FIGS. 9, 10 and 11, the refinement processrequires the interpolation computations in the number of about(2+2Ns/Ng).times.(m.times.m−1) for each pixel on the reference image R.This number is approximately (2+2Ns/Ng) times greater than the number ofinterpolation computations required for the first embodiment shown inFIG. 5. Since there is no need of a memory for storing the whole of thehigh-resolution reference image F′, however, the total memory capacityrequirement can be reduced.

Taking into consideration the facility of multiply and divide operationsin a circuit, m1 and m2 are preferably a power of 2. With the reductionin the magnitude of m1 and m2, the circuit scale can be reduced. On theother hand, the approximation accuracy of the coordinate (motion vector)for motion estimation is adversely affected, and the prediction error islikely to be inverted in magnitude in the computation of Equation 1. Theresult of motion estimation thus is distorted, thereby deteriorating theperformance of prediction. With the increase of m1 and m2, by contrast,the inverse phenomenon results. Taking the circuit scale intoconsideration, the m1 or m2 value of 4 or less is desirable. When theperformance of prediction is taken into account, however, 2 or more is adesirable value of m1 and m2. Balancing between these two extremes, theappropriate value of m1 and m2 is 2 and 4 respectively.

When motion estimation is carried out using a high-resolution referenceimage R′ with an image density of m times larger in horizontal andvertical directions, the value of the transformation functions fi(x,y)and gi(x,y) in Equations 5 to 7 is limited to an integer multiple of1/m. In other words, this indicates that the minimum unit of thetransformation function becomes 1/m of the interval between adjacentpixels. This restriction, however, is applied only to the motionestimation, and need not be observed in synthesizing the predicted imageP. In the motion compensation based on spatial transformation, on theother hand, in order to prevent a mismatch of predicted images P in thevideo coder 1 at the sending end and in the video decoder 2 at thereceiving end, some standard is required to be established with respectto the computation accuracy of the transformation function forsynthesizing the predicted image P. One method of establishing such astandard is by setting a minimum unit of the transformation function forsynthesizing the predicted image P as in motion estimation.

In this method, the horizontal and vertical components of the motionvector of each pixel used in synthesizing the predicted image P at thesynthesis circuit 4-1 of the video coder 1 and the synthesis circuit 4-2of the video decoder 2 are specified to assume only a value equal to aninteger multiple of 1/d1 and 1/d2 (d1 and d2 are positive integers)respectively of the distance between adjacent pixels. In other words,the synthesis circuits 4-1 and 4-2 are constructed to include means forrounding the computation result of the transformation functions fi(x,y)and gi(x,y) into a value equal to an integer multiple of 1/d1 and avalue equal to an integer multiple of 1/d2, respectively.

With reference to the case using the affine transformation (Equation 5)as a transformation function, explanation will be made below about anembodiment of a method in which the computation result of thetransformation function is rounded into a value equal to an integermultiple of 1/d1 and 1/d2. For simplicity's sake, it is assumed thatd1=d2=d (d: positive integer). It is also assumed that the patch istriangular in shape and that the motion vectors of three vertices of thepatch are transmitted as motion information.

The following description deals with the example shown in FIG. 12. Apatch 1202 in the reference image R1201 is estimated to have beentranslated and deformed to a patch 1207 of a current frame 1206. Gridpoints 1203, 1204, 1205 correspond to grid points 1208, 1209, 1210,respectively. In the process, it is assumed that the coordinates of thevertices 1203, 1204, 1205 of the patch 1202 are (x1′, y1′), (x2′, y2′),(x3′, y3′) respectively, and the coordinates of the vertices 1208, 1209,1210 of the patch 1207 are (x1, y1), (x2, y2), (x3, y3), respectively.All the coordinate values are assumed to be an integral value notnegative. The motion parameter aij of Equation 5 for this patch can beexpressed as (ai.times..times.1 ai.times..times.4 ai.times..times.2ai.times..times.5 ai.times..times.3ai.times..times.6)=1Di.times.(y.times..times.2−y.times..times.3 y.times..times.3−y.times..times.1y.times..times.1−y.times..times.2 x.times..times.3−x.times..times.2x.times..times.1−x.times..times.3x.times..times.2−x.times..times.1x.times..times.2.times.y.times..times.2−x.times..times.3.times.y.times..times.2x.times..times.3.times.y.times..times.1−x.times..times.1.times.y.times..times.3x.times..times.1.times.y.times..times.2−x.times..times.2.times.y.times..times.1).times.(x.times..times.1′y.times..times.1′x.times..times.2′y.times..times.2′x.times..times.3′y.times..times.3′).times..times.Di=x.times..times.1.times.(y.times..times.2−y.times..times.3)−y.times..times.1.times.(x.times..times.2−x.times..times.3)+(x.times..times.2.times.y.times..times.3−x.times..times.3.times.y.times..times.2) (9) In this equation, anydividing operation is not performed and aij (j: 1 to 6) is retained inthe form of aij=aji′/Di where both the numerator and denominator are aninteger. Then, the computation result of Equation 5 can always be givenin the form of a fraction having a numerator and a denominator of anintegral number such as fi(x,y)=fi′(x,y)/Di and gi(x,y)=gi′(x,y)/Di.Defining the symbol “//” as representing a dividing operation betweenintegral values (a dividing operation in which the decimal component ofthe computation result is discarded), it is assumed that Fi.function.(x,y)=1d.times.{(dfi′.function.(x,y)+ki)//Di}.times..times.Gi.function.(x,y)=1d.times.{(dgi′.function.(x,y)+ki)//Di} (10)whereki=Di//2. Fi(x,y) and Gi(x,y) are the functions for rounding fi(x,y) andgi(x,y) respectively into a value equal to the nearest integer multipleof 1/d.

In the synthesis circuit 4-1 of the video coder 1 and the synthesiscircuit 4-2 of the video decoder 2, if Fi(x,y) and Gi(x,y) of Equation 7are used in place of fi(x,y) and gi(x,y) of Equation 4, the horizontaland vertical components of the motion vector of each pixel can berestricted to assume only a value equal to an integer multiple of 1/d ofthe distance between adjacent pixels. Also, by using Fi(x,y) and Gi(x,y)for both the sending and the receiving ends, a mismatch of the predictedimage P attributable to the error of the transformation function can beprevented in a computation comparatively low in accuracy.

FIG. 13 shows the flow of operation for computing Fi(x,y) and Gi(x,y)when d=4 at the synthesis circuits 4-1, 4-2. First, when the coordinateof vertices of a patch before and after deformation are given at step1301, functions fi′(x,y) and gi′(x,y) are defined at steps 1302 and1304, a constant Di is determined at step 1303, and a constant kidetermined at step 1305. Using these functions and constants, the valuesof Fi(x,y) and Gi(x,y) are calculated from the coordinate (x,y) for eachpixel in the patch. When (x,y) is given in a binary integral notation,first, step 1306 computes the sum of products to determine the value offi′(x,y) and gi′(x,y), the result of which is shifted to the left by twobits at step 1307 into a value four (=d) times as large. This result isadded to ki at step 1308, and further is divided by Di at step 1309 (thefigures of the computation result below the decimal point arediscarded), thereby determining the values of 4Fi(x,y) and 4Gi(x,y).With these integral numbers of 4Fi(x,y) and 4Gi(x,y), step 1310 sets thedecimal point between the second and third digits from the low-orderplace. The values of Fi(x,y) and Gi(x,y) can thus be obtained. This hasthe same meaning as having carried out the operation of dividing by 4.

The value d can be either defined as a fixed parameter for thecoding/decoding system, or can be determined as a variable byarrangement between the sending and the receiving ends beforetransmitting the video data. An example procedure for determining thevalue d by communication between the video coder 1 at the sending endand the video decoder 2 at the receiving end is shown in FIG. 14. First,step 1403 causes the sending end to notify the receiving end bycommunication that the allowable upper limit of d is 4 due to thehardware restriction of the video coder 1. Then, the receiving end atstep 1404 notifies the sending end by communication that the upper limitof d is 2 due to the restriction of the video coder 2. As a result, thesending end decides that the optimum value of d is 2 and gives advice atstep 1405 that the video data subsequently transmitted is coded with das 2. Immediately after this advice, the sending end transmits videodata at step 1406. Generally, the larger the value d, the morecomplicated the system hardware. Consequently, it is consideredappropriate that the sending end employs the upper limit value for thesending or receiving end, whichever is lower.

For this method to be realized, the video coder 1 and the video decoder2 are required to have a function capable of accommodating the value ofd equal to or lower than their own upper limit respectively.

Considering the facility of multiply and divide operation, a power of 2is recommendable as the value of d. The larger the value of d, thesmaller the prediction error. In spite of this, the synthesizing processfor the predicted image P becomes more complicated. Taking theperformance of prediction into consideration, the desirable value of dis 2 or more. As a trade-off between the performance of prediction andthe complication of the process, an appropriate value of d isspecifically 2, 4, 8.

The following-described modifications also obviously are included in thepresent invention.

(1) Instead of the bilinear interpolation (Equation 2) employed in thepresent specification as a function for interpolation of the luminancevalue, other functions may be used with equal effect. With the increasein the complexity of a function, the advantage is enhanced for reducingthe required number of interpolations

(2) Also, instead of the affine transformation (Equation 5) which wasemphasized in the present specification as a type of transformationfunction, other transformation functions (Equation 6 or 7) may be usedwith equal effect. The present invention remains effective as far as thepixels in the same patch need not follow a common motion vector and thevertical and horizontal components of the motion vector of a pixel canassume a value other than an integer multiple of the distance betweenadjacent pixels. Also, the invention is effective as far as thecomputation result of a transformation function can change according tothe computation accuracy thereof.

(3). The patch can be of any shape that defines a set of pixels and isnot necessarily a triangle as described in the present specification.

(4) With regard to the motion compensation based on spatialtransformation, a method is taken up in the present specification inwhich the motion vector changes continuously at the boundary of a patch.In spite of this, an alternative method may be employed in which themotion parameter is transmitted directly for each patch or thediscontinuity of the motion vector at the patch boundary is otherwiseallowed.

(5) Although the present specification employs the block matching andthe hexagonal matching as a motion estimation algorithm, a method basedon other matching schemes may be used with equal effect. The presentinvention is effective in any method in which the prediction error isevaluated a multiplicity of times.

(6) In the motion compensation based on spatial transformation, themotion information transmitted may be other than motion vectors of patchvertices (grid points) as in the case of the present specification. Anymotion information may be used which specifies the transformationfunction for each patch. The motion parameter aij of Equation 5, forexample, may be transmitted directly. In the case where a motionparameter is transmitted directly in this way, the application of thisinvention makes it possible to reduce the accuracy of the motionparameter (to reduce the number of digits) transmitted while preventinga mismatch of the predicted image attributable to the computationaccuracy of a transformation function. The smaller the value of d, theless the number of digits required of the motion parameter, with theresult that the amount of transmitted information can be reduced.

(7) The values of m1 and m2, which are equal to each other in theembodiment described above, may alternatively be not equal to eachother.

(8) Unlike in this embodiment representing a case where the values of d1and d2 are equal to each other, they may be different from each other.

(9) The present specification deals with a method in which the patchstructure of the current frame is fixed and the patch of a referenceimage is deformed. Nevertheless, a method may alternatively be used inwhich the patch structure of a reference image is fixed while the patchof the current frame is deformed.

(10) Unlike in the present specification employing a single referenceimage for synthesizing a single predicted image, a plurality ofreference images may be used with equal effect.

According to the present invention, it is possible to reduce the numberof computations for interpolation of luminance values in the motionestimation process for a motion compensation scheme in which all thepixels associated with the same patch are not restricted to have acommon motion vector but the horizontal and vertical components of themotion vector of pixels can assume an arbitrary value other than aninteger multiple of the distance between adjacent pixels.

Further, according to the present invention, the computation accuracy ofthe transformation function can be reduced while preventing a mismatchof the predicted image in synthesizing a predicted image by a motioncompensation scheme in which all the pixels associated with the samepatch are not restricted to have a common motion vector and thehorizontal and vertical components of the motion vector of pixels canassume an arbitrary value other than an integer multiple of the distancebetween adjacent pixels. Furthermore, in a method of determining thevalues of d1 and d2 by arrangement between the sending and receivingends before transmission of video data, an optimum image quality of adecoded image can be determined in accordance with the performance ofthe systems at the sending end and the receiving end.

1. A video decoder comprising: means for receiving information of motionvectors of vertices of a patch which composes an image being decoded andinformation specifying that values of horizontal and vertical componentsof said motion vector for each pixel in said patch are limited tointegral multiples of 1/d1 and 1/d2 of the distance between adjacentpixels, where d1 and d2 are integers not less than 2; and means forcalculating a motion vector for each pixel in said patch from saidmotion vectors of vertices of a patch, limiting the horizontal andvertical components of said motion vector for each pixel to integralmultiples of said 1/d1 and 1/d2, and synthesizing said image beingdecoded by using said motion vector for each pixel.